Practice Degree (2.1) - Cubic Functions - IB 10 Mathematics

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the degree of the function $f(x) = 4x^3 + 2x$ ?
Show hintHide hint
Look for the term with the biggest exponent.
Question 2.
True or False: A cubic function can have four real roots.
Show hintHide hint
Think about the maximum number of times a cubic function can cross the x-axis.
3Question 3.
What is the maximum number of real roots a cubic function can have?
- 1
- 2
- 3
- 4
Show hintHide hint
Remember the highest degree defines the maximum number of x-intercepts.
4Question 4.
True or False: A cubic function always has at least one real root.
- True
- False
Show hintHide hint
Think about the nature of continuous functions.
Question 5.
Given the function $f(x) = 3x^3 - 12x + 9$ , find its real roots and describe the graph.
Show hintHide hint
Use x-value substitution to determine roots and sketch based on end behavior.
Question 6.
Analyze the end behavior for the cubic function $f(x) = -2x^3 + 5x^2 + 4$ . Explain what happens as x approaches infinity and negative infinity.
Show hintHide hint
Look at the leading coefficient's sign to predict the graph's direction.

5 more questions in this section. Enroll free to practise them all.